That's what outspoken billionaire Carl Icahn has told the company in an open letter, saying the board of the tech giant is doing shareholders a "great disservice" by refusing to buy back shares in the company.

"In our opinion, a great example of a 'no brainer' in today's market is Apple," the 77-year-old self-made billionaire wrote in an open letter to shareholders this week.

He said the company currently has a "dramatic valuation disconnect" between the price of the shares and their actual value and is urging the board to buy back shares in the company - effectively investing in themselves - to boost the value.

"No one on the Board seems to be an expert in the world of investment management. However, based on our record, we believe few will argue that we are experts in this area, and we have no doubts that the Board is doing a great disservice to its shareholders by not immediately increasing the size of the share repurchase program in order to more effectively take advantage of what we believe to be the company's low market valuation," the immodest billionaire said.

The public missive comes as Mr Icahn invested another $500 million in Apple shares overnight, his second spree in recent weeks where he has dropped $1 billion on Apple stock to raise his total holdings in the company to $3.6 billion. That represents a stake of less than 1 per cent in Apple, which has a market value of about $500 billion.

Bought another $500mil of $AAPL tday, bringing our total to $3.6 billion. If board doesn't see AAPL's 'no brainer' value we sure do.